The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  1  0  1 X^2 X^2  1  X  1  X X^2  1 X^2  0  1  X  1  1  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X X^2 X^2  X  0 X^2  X X^2+X X^2  X X^2+X  0  X  X X^2+X  X  0  X  X X^2+X  X  X X^2 X^2+X X^2 X^2  0 X^2 X^2  0 X^2+X X^2  0  0  0
 0  0  X  0  0  0  X X^2+X  X  X  X  0  0  X X^2  X X^2  X X^2+X X^2 X^2+X  0 X^2 X^2  X  X X^2 X^2  0  0  0 X^2 X^2 X^2+X X^2 X^2+X X^2+X  0 X^2  X  X  X  X  X X^2+X  0
 0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2+X X^2+X  X  X  X  0 X^2+X  0  X  X  X X^2+X X^2  X  0  0 X^2+X  X X^2+X  0  0  0 X^2 X^2+X X^2+X  0  X  0
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  0 X^2+X  X X^2  X  X X^2 X^2+X  0  0  0 X^2+X  X X^2+X X^2 X^2+X  X X^2+X X^2 X^2  X  0 X^2+X  0  0  X  0  X X^2+X  X X^2+X  X  X  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0

generates a code of length 46 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+58x^38+86x^39+147x^40+184x^41+222x^42+352x^43+385x^44+426x^45+476x^46+422x^47+362x^48+340x^49+176x^50+126x^51+127x^52+60x^53+53x^54+36x^55+34x^56+12x^57+6x^58+2x^59+2x^61+1x^70

The gray image is a linear code over GF(2) with n=184, k=12 and d=76.
This code was found by Heurico 1.16 in 0.777 seconds.